UNDRAINED CAVITY EXPANSIONS IN CRITICAL STATE SOILS
Boundary value problems for hardening/softening soils, such as Cam‐Clay, usually require the extensive use of finite element methods. Here analytical and semi‐analytical solutions for the undrained expansion of cylindrical and spherical cavities in critical state soils are presented. The strain is f...
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| Published in: | International journal for numerical and analytical methods in geomechanics Vol. 20; no. 7; pp. 489 - 516 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Sussex
John Wiley & Sons, Ltd
01.07.1996
Wiley |
| Subjects: | |
| ISSN: | 0363-9061, 1096-9853 |
| Online Access: | Get full text |
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| Abstract | Boundary value problems for hardening/softening soils, such as Cam‐Clay, usually require the extensive use of finite element methods. Here analytical and semi‐analytical solutions for the undrained expansion of cylindrical and spherical cavities in critical state soils are presented. The strain is finite, the initial cavity radius is arbitrary and the procedure applicable to any isotropically hardening materials. In all cases only simple quadratures are involved, and in the case of the original Cam‐Clay a complete analytical solution can be found. In addition to providing models of the behaviour of displacement piles and pressuremeters these results also provide valuable benchmark solutions for verifying various numerical methods. |
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| AbstractList | Boundary value problems for hardening/softening soils, such as Cam-Clay, usually require the extensive use of finite element methods. Here analytical and semi-analytical solutions for the undrained expansion of cylindrical and spherical cavities in critical state soils are presented. The strain is finite, the initial cavity radius is arbitrary and the procedure applicable to any isotropically hardening materials. In all cases only simple quadratures are involved, and in the case of the original Cam-Clay a complete analytical solution can be found. In addition to providing models of the behaviour of displacement piles and pressuremeters these results also provide valuable benchmark solutions for verifying various numerical methods. |
| Author | COLLINS, I. F. YU, H. S. |
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| Cites_doi | 10.1002/nag.1610080203 10.1680/geot.1985.35.2.99 10.1680/geot.1994.44.1.21 10.1016/0266-352X(92)90022-L 10.1002/nag.1610030402 10.1002/nag.1610191104 10.1002/nag.1610020107 10.1093/qjmam/12.1.52 10.1680/geot.1977.27.4.455 10.1680/geot.1989.39.4.679 10.1680/geot.1991.41.3.341 10.1061/JSFEAQ.0001740 10.1680/geot.1979.29.4.361 10.1002/nag.1610160103 10.1680/geot.1986.36.3.349 10.1016/0020-7403(89)90027-1 10.1061/JSFEAQ.0000524 10.1680/geot.1991.41.2.173 10.1061/(ASCE)0733-9410(1994)120:12(2118) |
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| Copyright | Copyright © 1996 John Wiley & Sons, Ltd. 1996 INIST-CNRS |
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| Keywords | Critical state Clay soil Modeling Finite element method Numerical analysis Consolidation Cavity Stress distribution Elastoplasticity Kinematics Pile Structure soil interaction Expansion sedimentary rocks overconsolidated materials underground cavities kinematics piles clastic sediments clay expansion |
| Language | English |
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| References | A. N. Schofield and C. P. Wroth, Critical State Soil Mechanics, McGraw-Hill, New York, 1968. D. Muir Wood, Soil Behaviour and Critical State Soil Mechanics, Cambridge University Press, Cambridge, 1990. M. Zytynski, M. F. Randolph, R. Nova and C. P. Wroth, 'On modelling the unloading-reloading behaviour of soils', Int. J. Numer Anal. Methods Geomech., 2, 87-93 (1978). H. S. Yu and G. T. Houlsby, 'A large strain analytical solution for cavity contraction in dilatant solis', Int. J. Numer. Anal. Meth. Geomech., 19, 793-811 (1995). J. P. Carter, J. R. Booker and S. K. Yeung, 'Cavity expansion in cohesive-frictional soils', Geotechnique, 36, 349-358 (1986). M. M. Baligh, 'Cavity expansion in sands with curved envelopes', J. Soil Mech. Found. Div. ASCE, 102, 1131-1146 (1976). M. F. Randolph, J. P. Carter and C. P. Wroth, 'Driven piles in clay-the effects of installation and subsequent consolidation', Geotechnique, 29, 361-393 (1979). M. R. Coop and C. P. Wroth, 'Field studies of an instrumented model pile in clay', Geotechnique, 39, 679-696 (1989). A. J. Bond and R. J. Jardine, 'Effect of installing displacement piles in a high OCR clay', Geotechnique, 41, 341-363 (1991). R. Hill, The Mathematical Theory of Plasticity, Oxford University Press, Oxford, 1950. H. S. Yu, 'State parameter from self-boring pressuremeter tests in sand', J. Geotech. Eng., ASCE, 120, 2118-2135 (1995). P. Chadwick, 'The quasi-static expansion of a spherical cavity in metals and ideal soils', Q. J. Mech. Appl. Math., 12, 52-71 (1959). D. Bigoni and F. Landuro, 'The quasi-static finite cavity expansion in a non standard elastoplastic medium', Int. J. Mech Sci., 31, 825-837 (1989). J. H. Atkinson and P. L. Bransby, The Mechanics of Soils, McGraw-Hill, New York, 1978. H. S. Yu and G. T. Houlsby, 'Finite cavity expansion in dilatant soil: loading analysis', Geotechnique, 41, 173-183 (1991). B. Ladanyi, 'Expansion of a cavity in a saturated medium', J. Soil Mech. Found. Div. ASCE, 89, 127-161 (1963). K. Been and M. G. Jefferies, 'A state parameter for sands', Geotechnique, 35, 99-112 (1985). J. O. M. Hughes, C. P. Wroth and D. Windle, 'Pressuremeter test in sands', Geotechnique, 27, 455-477 (1977). I. F. Collins and J. R. Stimpson, 'Similarity solutions for drained and undrained cavity expansions of soils', Geotechnique, 44, 21-34 (1994). I. F. Collins, M. J. Pender and Yang Wang, 'Cavity expansion in sands under drained loading conditions', Int. J. Numer. Anal. Methods Geomech., 16, 3-23 (1992). J. P. Carter, M. F. Randolph and C. P. Wroth, 'Stress and pore pressure changes in clay during and after the expansion of a cylindrical cavity', Int. J. Numer. Anal. Meth. Geomech., 3, 305-323 (1979). R. O. Davis, R. F. Scott and G. Mullenger, 'Rapid expansion of a cylindrical cavity in a rate type soil', Int. J. Numer. Anal. Methods Geomech., 8, 3-23 (1984). R. E. Gibson and W. F. Anderson, 'In situ measurement of soil properties with the pressuremeter', Civil Eng. Public Works Rev. 56, 615-618 (1961). H. S. Yu, 'Expansion of a thick cylinder of soils', Comput. Geotechnics, 14, 21-41 (1992). A. S. Vesic, 'Expansion of cavities in infinite soil mass', J. Soil Mech. Found. Div. ASCE, 98, 265-290 (1972). 1976; 102 1963; 89 1977; 27 1986; 36 1994; 44 1978; 2 1950 1992; 14 1995; 19 1992; 16 1961; 56 1979 1978 1979; 29 1989; 31 1990 1991; 41 1984; 8 1979; 3 1972; 98 1995; 120 1994; 2 1968 1959; 12 1985; 35 1989; 39 Yu (10.1002/(SICI)1096-9853(199607)20:7<489::AID-NAG829>3.0.CO;2-V-BIB19) 1995; 120 Wroth (10.1002/(SICI)1096-9853(199607)20:7<489::AID-NAG829>3.0.CO;2-V-BIB28) 1979 Coop (10.1002/(SICI)1096-9853(199607)20:7<489::AID-NAG829>3.0.CO;2-V-BIB26) 1989; 39 Carter (10.1002/(SICI)1096-9853(199607)20:7<489::AID-NAG829>3.0.CO;2-V-BIB12) 1979; 3 Randolph (10.1002/(SICI)1096-9853(199607)20:7<489::AID-NAG829>3.0.CO;2-V-BIB13) 1979; 29 Kirby (10.1002/(SICI)1096-9853(199607)20:7<489::AID-NAG829>3.0.CO;2-V-BIB25) 1979 Chadwick (10.1002/(SICI)1096-9853(199607)20:7<489::AID-NAG829>3.0.CO;2-V-BIB1) 1959; 12 Yu (10.1002/(SICI)1096-9853(199607)20:7<489::AID-NAG829>3.0.CO;2-V-BIB9) 1991; 41 Yu (10.1002/(SICI)1096-9853(199607)20:7<489::AID-NAG829>3.0.CO;2-V-BIB10) 1992; 14 Been (10.1002/(SICI)1096-9853(199607)20:7<489::AID-NAG829>3.0.CO;2-V-BIB16) 1985; 35 Zytynski (10.1002/(SICI)1096-9853(199607)20:7<489::AID-NAG829>3.0.CO;2-V-BIB24) 1978; 2 Vesic (10.1002/(SICI)1096-9853(199607)20:7<489::AID-NAG829>3.0.CO;2-V-BIB4) 1972; 98 Bond (10.1002/(SICI)1096-9853(199607)20:7<489::AID-NAG829>3.0.CO;2-V-BIB27) 1991; 41 Atkinson (10.1002/(SICI)1096-9853(199607)20:7<489::AID-NAG829>3.0.CO;2-V-BIB22) 1978 Hill (10.1002/(SICI)1096-9853(199607)20:7<489::AID-NAG829>3.0.CO;2-V-BIB29) 1950 Hughes (10.1002/(SICI)1096-9853(199607)20:7<489::AID-NAG829>3.0.CO;2-V-BIB6) 1977; 27 Yu (10.1002/(SICI)1096-9853(199607)20:7<489::AID-NAG829>3.0.CO;2-V-BIB11) 1995; 19 Baligh (10.1002/(SICI)1096-9853(199607)20:7<489::AID-NAG829>3.0.CO;2-V-BIB5) 1976; 102 Ladanyi (10.1002/(SICI)1096-9853(199607)20:7<489::AID-NAG829>3.0.CO;2-V-BIB3) 1963; 89 Carter (10.1002/(SICI)1096-9853(199607)20:7<489::AID-NAG829>3.0.CO;2-V-BIB7) 1986; 36 Collins (10.1002/(SICI)1096-9853(199607)20:7<489::AID-NAG829>3.0.CO;2-V-BIB14) 1992; 16 Bigoni (10.1002/(SICI)1096-9853(199607)20:7<489::AID-NAG829>3.0.CO;2-V-BIB8) 1989; 31 Schofield (10.1002/(SICI)1096-9853(199607)20:7<489::AID-NAG829>3.0.CO;2-V-BIB21) 1968 Collins (10.1002/(SICI)1096-9853(199607)20:7<489::AID-NAG829>3.0.CO;2-V-BIB17) 1994; 44 Yu (10.1002/(SICI)1096-9853(199607)20:7<489::AID-NAG829>3.0.CO;2-V-BIB20) Collins (10.1002/(SICI)1096-9853(199607)20:7<489::AID-NAG829>3.0.CO;2-V-BIB15) 1994; 2 Davis (10.1002/(SICI)1096-9853(199607)20:7<489::AID-NAG829>3.0.CO;2-V-BIB18) 1984; 8 Gibson (10.1002/(SICI)1096-9853(199607)20:7<489::AID-NAG829>3.0.CO;2-V-BIB2) 1961; 56 Wood (10.1002/(SICI)1096-9853(199607)20:7<489::AID-NAG829>3.0.CO;2-V-BIB23) 1990 |
| References_xml | – reference: A. J. Bond and R. J. Jardine, 'Effect of installing displacement piles in a high OCR clay', Geotechnique, 41, 341-363 (1991). – reference: A. N. Schofield and C. P. Wroth, Critical State Soil Mechanics, McGraw-Hill, New York, 1968. – reference: H. S. Yu, 'State parameter from self-boring pressuremeter tests in sand', J. Geotech. Eng., ASCE, 120, 2118-2135 (1995). – reference: M. Zytynski, M. F. Randolph, R. Nova and C. P. Wroth, 'On modelling the unloading-reloading behaviour of soils', Int. J. Numer Anal. Methods Geomech., 2, 87-93 (1978). – reference: H. S. Yu and G. T. Houlsby, 'Finite cavity expansion in dilatant soil: loading analysis', Geotechnique, 41, 173-183 (1991). – reference: D. Bigoni and F. Landuro, 'The quasi-static finite cavity expansion in a non standard elastoplastic medium', Int. J. Mech Sci., 31, 825-837 (1989). – reference: R. E. Gibson and W. F. Anderson, 'In situ measurement of soil properties with the pressuremeter', Civil Eng. Public Works Rev. 56, 615-618 (1961). – reference: R. Hill, The Mathematical Theory of Plasticity, Oxford University Press, Oxford, 1950. – reference: M. R. Coop and C. P. Wroth, 'Field studies of an instrumented model pile in clay', Geotechnique, 39, 679-696 (1989). – reference: H. S. Yu, 'Expansion of a thick cylinder of soils', Comput. Geotechnics, 14, 21-41 (1992). – reference: K. Been and M. G. Jefferies, 'A state parameter for sands', Geotechnique, 35, 99-112 (1985). – reference: J. O. M. Hughes, C. P. Wroth and D. Windle, 'Pressuremeter test in sands', Geotechnique, 27, 455-477 (1977). – reference: B. Ladanyi, 'Expansion of a cavity in a saturated medium', J. Soil Mech. Found. Div. ASCE, 89, 127-161 (1963). – reference: J. P. Carter, M. F. Randolph and C. P. Wroth, 'Stress and pore pressure changes in clay during and after the expansion of a cylindrical cavity', Int. J. Numer. Anal. Meth. Geomech., 3, 305-323 (1979). – reference: M. F. Randolph, J. P. Carter and C. P. Wroth, 'Driven piles in clay-the effects of installation and subsequent consolidation', Geotechnique, 29, 361-393 (1979). – reference: M. M. Baligh, 'Cavity expansion in sands with curved envelopes', J. Soil Mech. Found. Div. ASCE, 102, 1131-1146 (1976). – reference: J. P. Carter, J. R. Booker and S. K. Yeung, 'Cavity expansion in cohesive-frictional soils', Geotechnique, 36, 349-358 (1986). – reference: R. O. Davis, R. F. Scott and G. Mullenger, 'Rapid expansion of a cylindrical cavity in a rate type soil', Int. J. Numer. Anal. Methods Geomech., 8, 3-23 (1984). – reference: P. Chadwick, 'The quasi-static expansion of a spherical cavity in metals and ideal soils', Q. J. Mech. Appl. Math., 12, 52-71 (1959). – reference: D. Muir Wood, Soil Behaviour and Critical State Soil Mechanics, Cambridge University Press, Cambridge, 1990. – reference: J. H. Atkinson and P. L. Bransby, The Mechanics of Soils, McGraw-Hill, New York, 1978. – reference: A. S. Vesic, 'Expansion of cavities in infinite soil mass', J. Soil Mech. Found. Div. ASCE, 98, 265-290 (1972). – reference: H. S. Yu and G. T. Houlsby, 'A large strain analytical solution for cavity contraction in dilatant solis', Int. J. Numer. Anal. Meth. Geomech., 19, 793-811 (1995). – reference: I. F. Collins, M. J. Pender and Yang Wang, 'Cavity expansion in sands under drained loading conditions', Int. J. Numer. Anal. Methods Geomech., 16, 3-23 (1992). – reference: I. F. Collins and J. R. Stimpson, 'Similarity solutions for drained and undrained cavity expansions of soils', Geotechnique, 44, 21-34 (1994). – volume: 39 start-page: 679 year: 1989 end-page: 696 article-title: Field studies of an instrumented model pile in clay publication-title: Geotechnique – volume: 8 start-page: 3 year: 1984 end-page: 23 article-title: Rapid expansion of a cylindrical cavity in a rate type soil publication-title: Int. J. Numer. Anal. Methods Geomech. – volume: 41 start-page: 341 year: 1991 end-page: 363 article-title: Effect of installing displacement piles in a high OCR clay publication-title: Geotechnique – year: 1968 – volume: 29 start-page: 361 year: 1979 end-page: 393 article-title: Driven piles in clay—the effects of installation and subsequent consolidation publication-title: Geotechnique – start-page: 335 year: 1979 end-page: 344 – volume: 16 start-page: 3 year: 1992 end-page: 23 article-title: Cavity expansion in sands under drained loading conditions publication-title: Int. J. Numer. Anal. Methods Geomech. – volume: 120 start-page: 2118 year: 1995 end-page: 2135 article-title: State parameter from self‐boring pressuremeter tests in sand publication-title: J. Geotech. Eng., ASCE – year: 1950 – volume: 89 start-page: 127 year: 1963 end-page: 161 article-title: Expansion of a cavity in a saturated medium publication-title: J. Soil Mech. Found. Div. ASCE – volume: 14 start-page: 21 year: 1992 end-page: 41 article-title: Expansion of a thick cylinder of soils publication-title: Comput. Geotechnics – volume: 19 start-page: 793 year: 1995 end-page: 811 article-title: A large strain analytical solution for cavity contraction in dilatant solis publication-title: Int. J. Numer. Anal. Meth. Geomech. – year: 1990 – volume: 41 start-page: 173 year: 1991 end-page: 183 article-title: Finite cavity expansion in dilatant soil: loading analysis publication-title: Geotechnique – volume: 12 start-page: 52 year: 1959 end-page: 71 article-title: The quasi‐static expansion of a spherical cavity in metals and ideal soils publication-title: Q. J. Mech. Appl. Math. – volume: 56 start-page: 615 year: 1961 end-page: 618 article-title: In situ measurement of soil properties with the pressuremeter publication-title: Civil Eng. 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| Snippet | Boundary value problems for hardening/softening soils, such as Cam‐Clay, usually require the extensive use of finite element methods. Here analytical and... Boundary value problems for hardening/softening soils, such as Cam-Clay, usually require the extensive use of finite element methods. Here analytical and... |
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| SubjectTerms | Applied sciences Buildings. Public works cavity expansion critical state models Earth sciences Earth, ocean, space Engineering and environment geology. Geothermics Engineering geology Exact sciences and technology Geotechnics normally and overconsolidated clays pile installation plasticity Structure-soil interaction |
| Title | UNDRAINED CAVITY EXPANSIONS IN CRITICAL STATE SOILS |
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